Statistics and Probability Answers

The time between shots at goal in a football (soccer) game, X, has an exponen-
tial distribution with a mean of 9 shots every twenty minutes. Determine the
following

a)What is the probability of the time between shots being greater than 5 minutes?
b) What is the probability of more than 20 shots in 40 minutes?
c) In 6 non-overlapping 5 minute intervals, what is the probability of at least
one 5 minute period with no shots at goal?

Four people decide to buy a bag of 56 silver coins. Each person
contributes the following:
John - $320
Tony - $300
Mike - $220
Luce - $160
Determine the apportionment using
1.Hamilton Method
2.Jefferson Method
3.Webster method

What is the probability of two people having the same birthday?

The probability that a Dr correctly diagnoses a particular illness is 0.7, given that the Dr makes an incorrect diagnoses, the probability that a patient enters a law suit is 0.9. what is the probability that the Dr makes an incorrect diagnoses and the patient sues?

Q1. A small bank has two cashiers dealing with customers wanting to withdraw or deposit cash. For each cashier, the time to deal with a customer is a random variable having a normal distribution with mean 150s and standard deviation 45s.
A. Find the probability that the time taken for a randomly chosen customer to be dealt with by a cashier is more than 180s.
B. One of the cashier deals with two customers, one straight after the other.

1. An LU professor is interested in whether there is a difference between undergraduate students and graduate students in the amount of time spent praying each day. The professor gathers information from random samples of undergraduate and graduate students on the LU campus. The amount of time praying is normally distributed and is measured on an interval/ratio scale.
Graduate Undergraduate
15 9
17 11
10 9
13 6
11 5
17 6

a. What statistical test should be used to analyze the data?

b. Is this a one- or two tailed test?

c. Identify H0 and Ha for this study.

d. Conduct the appropriate analysis. Should H0 be rejected?

A random sample of 90 students at a private high school is tested and a mean SAT score of 1030 is obtained. The average score for public high school student is 1000 (σ= 200).

Compute Z obt

3. A researcher hypothesizes that people who listen to music via headphones have greater hearing loss and will thus score lower on a hearing test than those in the general population. On a standard hearing test, the overall mean for the general population is 22.5. The researcher gives this same test to a random sample of 12 individuals who regularly use headphones. Their scores on the test are 15, 14, 20, 20, 25, 22, 21, 19, 16, 17, 21, 22.


c. What are H0 and Ha for this study?

d. Compute t obt

e. Should H0 be rejected? What should the researcher conclude?

A researcher hypothesized that the pulse rates of long-distance athletes differ from those of other athletes. He believed that the runners’ pulses would be slower. He obtained a random sample of 10 long-distance runners. He measured their resting pulses. Their pulses were 45, 45, 64, 50, 58, 49, 47, 55, 50, 52 beats per minute. The average resting pulse of athletes in the general population is normally distributed with a pulse rate of 60 beats per minute.


c. What are H0 and Ha for this study?

d. Find tcv from appendix A in Jackson’s text.

e. Compute t obt

f. Should H0 be rejected? What should the researcher conclude?

1. A researcher is interested in whether students who attend private high schools have higher average SAT Scores than students in the general population. A random sample of 90 students at a private high school is tested and and a mean SAT score of 1030 is obtained. The average score for public high school student is 1000 (σ= 200).


b. What are H0 and Ha for this study?

c. Compute Z obt

d. What is the Z critical value (Z cv ) using a 0.05 alpha level?

e. Should H0 be rejected? What should the researcher conclude?

f. Determine the 95 % confidence interval for the population mean, based on the sample mean.